Fister, 29, went 14-9 with a 3.67 ERA in 33 games this past season, his third with the Tigers. Fister tied for the American League lead in getting batters to hit into double plays. He allowed 0.6 home runs per nine innings, second best in the AL.
The 6-foot-8 Fister fared well in the postseason, even after he was hit in the head by a line drive. He shook off the scary moment in Game 2 of the 2012 World Series against San Francisco and took a shutout bid into the seventh inning in what ended up being a 2-0 loss to the Giants. Over three postseasons with the Tigers, Fister had a 2.98 ERA in seven starts and a relief appearance.
Tigers GM Dave Dombrowski said the Tigers would move Drew Smyly into the rotation in place of Fister, who will likely replace Dan Haren in the Nationals' rotation and join Stephen Strasburg, Jordan Zimmermann and Gio Gonzalez.
The Tigers figure to save about $6 million by trading Fister, who was arbitration-eligible and projected to earn about $7 million. But Dombrowski said the trade was not done to save money in hopes of keeping Scherzer beyond next season.
"It gives us some flexibility for some other things we want to do," he said on a conference call.
Lombardozzi and Krol would project to earn approximately $1 million between them. And Ray is expected to start next season in the minors.
"This is an exciting day for the Washington Nationals," Rizzo said Monday in a statement. "We feel we've added a talented, young veteran to our starting pitching corps. Doug is battle-tested through playoff experiences, and the depth he brings to our staff is exceptional. We are thrilled to welcome him aboard."
The Tigers had been talking to other clubs about Fister, Scherzer and Porcello this winter. Scherzer is a Scott Boras client who is one year from free agency. But it's still unclear if they will be able to find common ground before Scherzer tests free agency next winter.
Dombrowski said dealing Fister did not have anything to do with his hope to give Scherzer a new contract before he becomes a free agent.
"I don't think that plays into it at all at this point," Dombrowski said.
Detroit has had an active offseason, and Dombrowski said he isn't done making moves, saying his top priority is to add a closer.
The Tigers traded first baseman Prince Fielder and his $214 million contract two weeks ago to the Texas Rangers in part to potentially save more than $75 million. They got second baseman Ian Kinsler for Fielder in a swap of All-Stars.
Detroit also allowed All-Star shortstop Jhonny Peralta to leave as a free agent for St. Louis. The Tigers replaced him with rookie Jose Iglesias just before Peralta was suspended for 50 games in the Biogenesis drug scandal.
"We're not cutting payroll whatsoever," Dombrowski said.
Dombrowski said he's not surprised at least some Tigers fans weren't happy when the trade was announced because the team traded the "known for the unknown."
"People in general don't like those type of moves," he said.
The 25-year-old Lombardozzi hit .259 with two homers and 22 RBIs in 118 games for the Nationals last season. The switch-hitter played 48 games at second base, 23 in left field and four at third base in 2013. He will replace Ramon Santiago on Detroit's roster.
"This was not an easy trade for [the Nationals] to make, either," Dombrowski said.
Krol made his major league debut in June for the Nationals after they acquired him from Oakland. The 22-year-old lefty was 2-1 with a 3.95 ERA in 32 games with Washington.
The 22-year-old Ray was 6-3 with a 3.11 ERA for Class A Potomac and was 5-2 with a 3.72 ERA for Double-A Harrisburg, giving the Tigers a pitcher they think will start the season at Triple-A Toledo with the ability to possibly pitch in the majors if needed in 2014. Baseball America rated him as the Nationals' No. 5 prospect.
"We are excited to be adding three solid players to the organization," Dombrowski said in a statement. "Robbie is a premium pitching prospect, Ian adds a quality left-handed young arm for the bullpen and Steve provides our ballclub with versatility in several roles as a switch-hitting utility man."
Information from ESPN's Jayson Stark and The Associated Press was used in this report.